Organization of the book

The book starts with generalizations of numbers (abstract algebra), moves to shapes (topology), and then adds geometric structure until arriving at fiber bundles. Each chapter of the book attempts to cover the following items:

Definitions of the main objects under study

Visualizations of the objects and their relationships

Related synonyms and jargon common to the literature

Statements of relevant facts and theorems

Since it is intended partly as a reference, an attempt is made to keep each section of the book as self-contained as possible. The topics are presented in an order designed to minimize any references to future material, and to a large extent this goal is attained. Nevertheless, the book is best read front to back, and results covered in one section are referred to in the sections that immediately follow without further comment.